Plickers!!! Remember your # No writing/tearing/bending Always return where they belong Let’s have fun with this!

Bellwork (1 of 3) Which of the following items was owned by the fewest U.S. homes in 1990? A. home computer B. CD player C. cordless phone D. dishwasher

Q #2 What is the slope of y=2x+5? 5 5/2 2/5 2

Q #3 What is the y-intercept of y=2/3x-6? -6 2/3 6 3/2

Solving Systems of Equations by Graphing Goals: ~Solve systems of equations by graphing ~Determine whether a system has 1, infinitely many, or no solutions

Key Term System of Equations: Two or more equations with the same variables

3 Possibilities… One solution No Solution Infinitely many solutions same line for both eqns

Steps to solve by graphing Put equations in slope-intercept form Graph: Plot the y-intercept then follow the slope ( ) to get the next point The intersection point is the solution Note: You can check by plugging your answer in

Basically… Get in y=mx+b form Graph Find intersection

Example 1: Solve by graphing. Y= -x+3 Y= 3/2x-2 Answer: 1. Both are already in slope-intercept form 2. Graph. Remember: y-int first then use slope to get next point 3. Find the intersection point. This is your solution.

Graph Solution is (2,1)

TRY IT! Solve by graphing… Y=x+2 Y=3x-2

Solution: (2,4)

Example 2: Solve by graphing 2x+y = 5 x – y = 1 Answer: Write each equation in slope-intercept form. 2x+y=5 --> y=-2x+5 x- y = 1 --> -y=-x+1 --> y=x-1 Graph. (Graph y-int then follow the slope[rise/run] to get the next point) The point where they cross is the solution

Graph (2,1) is the solution.

Answer: They cross only once so the solution is (2,1)

TRY IT! Solve by graphing… 2x-y= -5 -2x-y= -1

Answer: (-1,3)

Infinitely many solutions: How to know how many answers there are just by looking at the system of linear equations One Solution: Different slope Infinitely many solutions: Same equations (same slopes and y-intercepts) No Solution (parallel): Same slope & different y-intercept

y = -x + 3 2y = -2x + 6 Solution : y = -x + 3 Example 3: Without graphing, write whether there will be one solution, infinitely many solutions, or no solutions y = -x + 3 2y = -2x + 6 Solution : Put in slope-intercept form Look at the slope and y-intercept to get solution. y = -x + 3

Answer They both make the same graph, so there are infinitely many solutions!! 

TRY IT! Without graphing, write whether there will be one solution, infinitely many solutions, or no solutions 2a. y = 3x + 2 y = 3x -5 2b y = ½ x -6 y = 4x + 10

Mr. Monroe bought 2 lbs of cheddar cheese and 3 lbs of turkey Mr. Monroe bought 2 lbs of cheddar cheese and 3 lbs of turkey. He paid $26.35. Ms. Stewart paid $18.35 for 1.5 lbs of cheese and 2 lbs of turkey. Write the system of equations. Let’s look at each person separately… Mr. Monroe: 2x+3y=26.35 Ms. Stewart 1.5x+2y=18.35 How would I start to try and solve this by graphing?